What is asymmetric relaxation backpropagation?
I'll give you my initial $0.02 for symmetric relaxation or relaxation in general in working with neural networks. The book covers 'Weight perturbation' and this is a basic outline of that. Say you want to host a wedding and every person gives you a 'must-have' list of requirements for them to attend. You can abide by all the requirements of each wedding guest or start 'uninviting' guests whose restrictions cause too many complications.
There are several kinds of relaxation. I've only used Lagrangian relaxation, so my experience is biased to that application. Think of it like this: you are traveling from New York to LA and you want to optimize for time, if you 'relax' the constraints, you can just fly instead of driving. This, however, creates an increased cost of the air ticket. By relaxing the constraints you remove the isolating requirement that you must travel by car.
Symmetric relaxation can be a challenging subject, so I'll include a few links academic research
Academic research arxiv.org is another site I use for research. Hope this helps.
I also found a link on Medium which is another good source for application, theory, and implementation of algorithms. Medium Lagrangian Relaxation